Powered by Bravenet Bravenet Blog

Subscribe to Journal

Saturday, November 22nd 2014

23:12

Vegetarian Meatmarket

  • STATE OF EXISTENCE: carnivorous

It just had to happen sooner or later.

30 years ago: I was driving along in our Chevy Vega 4-door station wagon, a wonderful car, well-suited for the universal speed limit of 55 mph during that time since one wouldn't dare drive it any faster. Not only that, but its radio was working as well. As I was tooling along, I was contemplating the phenomenon of people looking at religion, specifically Christianity, as a means to get ahead in the material world. Right about then the man on the radio read his little commercial for So-and-so's Meatmarket (no longer in existence, I'm afraid). An image popped into my head of the church as an institution existing solely in order to give everyone whatever makes them the most comfortable---kind of like a vegetarian meatmarket. The song virtually wrote itself. It's always been one of my favorites, right up there with the poetry and music I had created a little earlier for June, casually known as the furniture moving song.

Four CowsToday: I took a pound of hamburger meat out of the freezer early this afternoon in order to use it for spaghetti sauce this evening. I quickly glanced at the label on the plastic wrapper and noticed that there was more information on it than the usual list of ingredients, and so I read it carefully. You might think that there should only be one ingredient listed, namely "ground beef," and that was, indeed, the case. However, the label also informed us of what was not included. For one thing, it did not have much fat. June and I prefer to get the lean variety, and I read that the distribution between "lean" meat and "fat" was 92% to 8%. Good. Lesser quality is cheaper, but what good is that when half of it just turns into grease. Still, we've only just begun with what other good news the label conveyed:

  • No added hormones ... Again good. Allegedly the injection of hormones into meat has played havoc with the bodies of some American children; for example, causing an earlier onset of puberty than in the past. I don't know enough to make a fully informed decision on the medical and physiological merits of that charge, but, all other things being equal, I'd just as soon have my meat without bovine growth hormones.
  • ... or antibiotics. That one puzzles me a little bit. I mean, if the cow gets sick wouldn't you want to give her whatever she needs to get better? My hunch is that some people may worry that antibiotics are over-prescribed in America anyway, and that adding them to our food will create such an overload in our bodies that we lose our natural internal immunities. So, presumably, some of those people try to avoid absorbing any antibiotics whatsoever, including ones that may be retained in the meat they ingest. Again, I must plead not having sufficient information at hand to make a firm ruling one way or the other, but I dislike the way people reduce such matters to a single possibility. Whether we take too many prescribed antibiotics on the whole is one question, and a good one. The likelihood that our own immune systems get overworked by consumption of artificially induced bovine antibodies, in lieu of those that the animal would have produced on its own anyway, is another matter, and it strikes me as fairly low. Then again, one wants the fewest amounts of added chemicals in one's meat, but it's a matter of finding the right balance. I prefer meat from healthy animals and with as few chemicals as possible. I don't think that one can (or should) reduce such issues to absolute one-sided declarations.
  • CowVegetarian Fed. This is the part that has me really, though figuratively, scratching my head (not literally ever since I switched to some awful-smelling tar-based shampoo). What is actually being said by that assertion? I'm ruling out immediately that the phrase is an abbreviation for "Vegetarian Federation" and thus might imply that this brand of ground beef is approved for vegetarians. That would be just a little too unusual, even in our world, as cluttered as it is with bizarre events, most of them documented faithfully on YouTube nowadays.
    • Conceivably, the phrase could be interpreted as meaning that only vegetarians were allowed to feed the cows that would ultimately wind up as ground beef. However, that idea comes with some serious issues as well. Please reflect on it: Would it really make a difference whether cows receive their daily hay from carnivores, herbivores, or omnivores? Wouldn't such a practice discriminate against people who eat meat? Why would one be in the beef business anyway if one objected to eating it?
    • So, I take it that it means that the cow has been on a vegetarian diet for all of her life. Okay, that claim would be a little more rational, but isn't that usually the case for cows? Remember that I was a zoology major in college (see my t-shirt in the video below), and I learned that cows are classified as grazers, viz. they eat grass and, should the friendly farmer supply it, corn. Grass and corn are forms of vegetation, so their natural diet is "vegetarian," though I must say that the adjective "vergetarian" is being used quite whimsically here. Cows are grazing herbivores, not "vegetarians." They don't eat meat; they don't like it, and they couldn't digest it if they did. Do other packages of meat come from carnivorous cows?
    • I have an odd feeling that there may be some more serious matter behind that assertion, and that maybe I should see if there's anything on the web about it. In the meantime, I suspect that this is as close as I shall ever come to seeing the concept of "vegetarian meat" exemplified in the real world.

So, here's the song. I'm afraid the quality of the recording has done nothing to enhance the quality of the one being recorded since I just did it on a whim tonight. It does fit into the category of "Lest I forget all of my songs." If you're looking for a Bible passage to go with it, be sure to turn to 2 Timothy 3:1-5.

 

2 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Thursday, November 20th 2014

20:48

Dominus Flevit

  • STATE OF EXISTENCE: somewhat dreary

A few thoughts on various things.

It has been a very slow week for me. It seems as though everything I'm doing takes three times the normal effort and time--when I can get myself to do it. But I know I'll get out of this hole again; it's just once again taking longer than I thought. These are my typical November feelings.

The first significant snowfall of this season has come and--remained. On Monday morning a good inch of the white stuff was sitting on vehicles that haven't been moved and on front lawns, and even the roads in town weren't cleared until Wednesday. Earlier in the week the temperatures were in the teens (°F), and we had single digits several nights. We are picking right back up where we left off not so long ago. It's only the middle of November, and we're already looking at January weather.

Saturday night was the last Cowboy Church of the "season." In previous years they did not take a break during winter, and, of course, the regular church itself (Trinity Methodist of Hartford City) will keep going. But after having to deal with blizzards and their ilk last year, the consensus was that there shouldn't be any Saturday night events for the next three months or so. The good thing about that decision is that I personally won't have to decide whether to drive out there on potentially bad evenings. The drawback is that I won't have it to decide about, and I will miss it greatly for this hiatus.  Last Saturday night went well, and, if I may say so myself, we finished with a good program. The regular crew was there, and there was a special guest group of about eight men (six guitars, one banjo, and one electric bass) and one woman vocalist. I'm afraid I don't remember their names either as a group or individuals. The lady's singing was of professional quality in the country gospel genre. Some of the other players were pretty good, though the gentleman playing the banjo pretty much dominated their presentation. One guitar player really stood out the two or three times that he was given about three bars of playing lead. Another one got some fascinating mandolin-style licks on his guitar. After their part of the program, when we all came together for a few songs, I let their bass player carry on and took the opportunity to play my harmonicas.

The following comments are not about any particular group, just a general observation by the curmudgeon in me, except insofar as they were sparked by the visiting group's self-reference as "bluegrass." It appears that nowadays any amateur group with limited vocal ability and either a banjo or mandolin among their instruments  calls itself "bluegrass." It doesn't work that way. Just as with any genre of music, there are "rules." Now, that's a funny way of putting it since obviously anybody is free to play whatever or however they want to. But to be called "bluegrass," a musical presentation should have certain characteristics. Bluegrass music, as it was formalized by Bill Monroe in the 1930's, developed on the radio, and it is extremely microphone centered. A description on Google Play summarizes that bluegrass music requires "a five-piece acoustic string band, playing precisely and rapidly, switching solos and singing in a plaintive, high lonesome voice." In other words, there are five or so musicians, playing typically a banjo, mandolin, guitar, fiddle, and string bass. Some of them may sing harmony with the main vocalist, following the traditional pattern of parallel fourths (C--F; D--G; A--D; etc.). In between the verses of the songs are lengthy musical interludes during which the player whose instrument is featured will step up to the mike and display his virtuosity. Brother-in-law Tom, who is (slowly) building his legend as mandolin phenom, told me that in a bluegrass setting the banjo and the mandolin never play melody lines simultaneously. When the banjo has its turn, the mandolin just keeps time with simple downward strums, and vice versa. In my observations, the guitar is frequently almost as much in the background as the bass. If the guitar player has a solo part, it usually consists of picking. Bill Monroe inspired a lot of enthusiasm for his new style, but he appeared to have been torn between wanting to have inaugurated a new genre and resenting any other bluegrass group as imitators.

In the video below Bill Monroe and the Bluegrass Boys are performing an instrumental number. So, you'll see how they take turns at the single microphone. YouTube has many more examples.

Switching topics rapidly again, I'm enjoying a number of ongoing back-and-forth matches of "Words with Friends" with friends on FB. My win-loss percentage is still heavily on the loss side, and I would have to win an enormous number of games without losing to bring it up to 50%, so I try to merely think in terms of playing against myself when I find that I'm 150 or more points behind my opponent halfway through a game. I have discovered (not that much of a search was necessary) that there are applications on the web that find words for you to your specification, as you input the letters available to you. Let me simply say that I won't use such a program, and I'm assuming that neither are my friends because that would make the game pointless.

Luke Bible Study

Read the Text!

Bible Reading:
Luke 19:41-44

v. 41: As He approached and saw the city, He wept over it. (HCSB)

The Mount of Olives faces the eastern side of Jerusalem. As I wrote the other day, it is right across from the Eastern Gate (The "Golden Gate") of the temple. Over the centuries many Jews have made a point out of being buried on the Mount of Olives so that they would be among the first who will rise and see the messiah enter Jerusalem by that gate. Of course, I can respond with the observation that, if they had been alive at the right moment, they would, indeed, have seen Jesus, the messiah, proceed along that path.

Dominus FlevitThe procession included a little interlude that Luke had not mentioned earlier. When Jesus had Jerusalem in full view, he stopped to weep over the city because he foresaw the destruction it would undergo. -- For the sake of anyone who might get confused on this bit of trivia, this verse is NOT the shortest verse in the Bible, "Jesus wept," which we find in John 11:35. The occasion that time was his grief over the death of Lazarus, whom he then resurrected. -- Here Jesus is showing his sadness for Jerusalem, knowing that it would not be too long before the city would be decimated, as happened in AD 70 by the hands of the Romans.

There is a little chapel on top of the Mount of Olives, called the Dominus Flevit Church. Dominus Flevit is Latin for "The Lord wept." The small building has the shape of a teardrop and is decorated with similar forms.

I don't want to get into any big issues right now, but just ask the question of myself as much as of you: Do we weep for the lost? I don't necessarily mean actual tears dripping out of our eyes, but simply a strong regret that they are missing out on the greatest gift in the world, eternal life. In many ways we have good reason to see various non-Christian persons, groups, or institutions as our "opponents,"given their actions. ISIS (ISIL) is just one extreme example. It's very hard to keep from getting carried away and letting our attitude turn into hatred. To be sure we must do what is necessary to defend those who cannot defend themselves, but we should do so with a heavy heart. Whether we're talking about the tortures carried out by Islamic extremists abroad or about hurdles erected by bureaucrats at home, let's not forget that, regardless of what they may get away with at the moment, they're on the losing side. There will be an end to their arrogance, and hopefully we have not become so inured that we don't feel sorry for them because of what their final fate will be.

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Sunday, November 16th 2014

11:39

The Return of Aïsha

  • STATE OF EXISTENCE: Okay
  • IN THE BACKDROP: Fossils and Foxes

The Return of Aïsha. I wrote and attempted to post this entry on Friday evening, but things went haywire with the transfer of coding once again so that I had to pull it immediately. Then I forgot about having withdrawn it and labored under the assumption that it was already there for the world to see. I'm retrying now on Sunday afternoon. It may come and go a few times over the next hour or so, but hopefully I can get my code to harmonize with Bravenet's expectations. Worst case scenario: If this means anything to you, I may have to rewrite everything in internal CSS format.

Leonhard Euler

A wonderful afternoon back at good old Taylor U. Kevin Diller, my successor as it were, had invited me to give a talk on militant Islam to his class on Western Religions. In the process, I also ran into some previous colleagues and some of those who would have been colleagues, had I been able to stay. The class room for the presentation was in the new (to me) Euler Science Complex. The name, by the way, is supposed to be pronounced “Yuhler,” not, as it would be in German, as “Oiler.” It is named after the donors of the building, not after the famous mathematician Leonhard Euler (1707 -1783), who is frequently ranked right at the top of the all-time field: Euclid, Pythagoras, Newton, Leibniz, Gauss, and Riemann--choose your order. Which is not to say that the donors do not deserve to have their name on the building or to have it pronounced in the form to which they are accustomed, but I also like the thought that Taylor might have named an academic building after a truly outstanding hero of academic history. One of L. Euler’s most beloved contributions is the equation that combines some of the most important constants in mathematics,

eπi +1=0.

where e (named after Euler) is the base of the natural logarithm, 2.718 ...,
π is the familiar 3.14...,
and i is the square root of -1, i. e. √- 1;
We should think of 1 as the "multiplicative identity constant" (i.e. any number multiplied by 1 remains the same),
and of 0 as the "additive identity constant" (i.e. any number plus 0 remains the same number).

The students in the class struck me as very much like the students I had to leave behind, friendly and clearly serious about learning—a wonderfully attentive audience. There’s not much one can cover in one class period; I basically gave the story of neo-Kharijite Islam, eventually leading up to ISIS. Most of what I said is contained in the material of my recent entry on ISIS. I stressed the historical background a little more perhaps than in that post. Needless to say, much of the content is contained in Neighboring Faiths, 2nd ed., except for ISIS, which was not yet in existence when I made the additions to the new edition. Also, just to add a slightly different angle, I tried as much as I could to observe the early history of the caliphate through the eyes of Aïsha, Muhammad’s young and spunky widow.

I alluded to Aïsha in the post to which I referred above. Let me add a few more details. As everyone knows (assuming the historicity of the hadith), Aïsha was betrothed to Muhammad at a very young age, and that the marriage was consummated when she was still far too young for such things by our standards. She was Muhammad’s favorite wife for the last nine years of his life, and she supported him publicly throughout that time. However, she had a head of her own right from the start and was not above criticizing the prophet himself in private, e.g., for him claiming to have had revelations that took him out of inconvenient situations. When Muhammad was on his death bed, the other wives conceded that he could stay in her quarters because they all knew that Muhammad and Aïsha had a special relationship, something that had been missing from his life during the most turbulent years of his career, which occurred (not without connection) after the death of his first wife, Khadija, his only wife as long as she lived. (There is actually no certainty on how many wives Muhammad had later on; 10 or 12 are popular options.)

After Muhammad’s death, Aïsha got involved in the ensuing political matters, particularly the issue of who would be the caliph (Muhammad’s successor for the community). That honor turned out to go to Abu Bakr, Aïsha’s father, so things went swimmingly for her for a while. She also approved of the second caliph, Umar (another father-in-law to Muhammad), but the political aspect of the Islamic world was heading towards great turmoil. Umar was assassinated, and the next caliph, Uthman, perhaps best known for collecting the authoritative edition of the Qur’an, was not as good a leader as his two predecessors. Uthman was of the clan of the Umayyads, who had not that long ago been Muhammad’s strongest opponents, and he lacked the charisma that would unite people under him. Aïsha took a strong dislike to Uthman because he apparently committed some acts of cruelty. However, when another man, namely the new Muslim official who was supposedly delegated to govern Egypt on behalf of the caliph, humiliated and eventually killed Uthman, she was outraged. Aïsha entertained a strong hope that the next caliph (Ali ben Talib) would avenge Uthman’s death. It was one thing to oppose him politically; it was quite another to mock and kill him and his wives. I’m not sure to what extent she communicated those thoughts to Ali, but it makes sense that she would have done so, if not in person, then at least by messenger.

Battle of the Camel

What made the matter awkward from Aïsha’s perspective was that she did not really care for Ali all that much either. For one thing he had been seeking the caliphate in competition with her father (Abu Bakr); for another his spine was just weak enough that he could be manipulated into changing his mind on crucial issues, sometimes as though it were on a whim at the very last moment before some action should have been taken. So, Aïsha may not have been surprised that Ali did not pursue those who had abused Uthman, and, as mentioned, she was furious with him. In the greater context, Ali’s most important opponent was a man named Muawiyah, another member of the Umayyad clan, who was basing his claim to be caliph on the simple notion that the Umayyads had always been the political leaders in Mecca and should continue along that line. Both Ali and Muawiyah were odious to Aïsha, but she was particularly angry at Ali for letting the mistreatment of one of Muhammad’s Companions (i.e. Uthman) go unpunished.

So, Aïsha, now around thirty years old, gathered an army to confront Ali and his followers in pitched battle. She personally served as commander of her troops, perching on top of a camel behind the lines so that she could have a clear view of the field and give orders as necessary. Thus, ever since then this encounter has been known as the “Battle of the Camel.” Sadly for Aïsha, Ali’s troops were stronger than hers, and she lost the battle. Ali’s men captured her, and Ali had her escorted back to Mecca. She remained there for a short while, and then moved back to her original home in Medina. Her days of political involvement were over, but she taught the message of the prophet and became one of the most important sources for the secondary writings concerning Muhammad, known as the hadith. (In case you were wondering earlier, that's how we know about some of her private conversations with her husband.)

From there, the story goes on as described in many places with the assassination of Ali by some Kharijites, the Umayyads hanging on to the caliphate for another century or so, and the permanent split between Sunna and Shi’a. And one other thing: Later on there have been some women who made contributions to Islamic culture in the subsequent history of Islam, but none with the genuine lasting impact of Aïsha.

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Thursday, November 13th 2014

21:20

A couple of quick updates

  • STATE OF EXISTENCE: headache

This entry will merely be an update on a couple of matters. My appointment yesterday with Dr. B went really well. He gave me exactly the reassurance I needed. Thanks for your prayers.

"Can you hear me now?" -- Probably not, and that's okay. More importantly, one of the items on our doctor's appointment list that I mentioned the other day was a visit for June to an audiologist on Monday. Yesterday morning she fitted her with a set of hearing aids, and suddenly she could once again hear things that she didn't even know were there. I wish everyone could have seen the look on her face when she wore a trial set just for a little while on Monday. The audiology doctor, let's call her Dr. D, asked her how she could have been functioning these last few years, a very pertinent question since she had about 90% loss in one ear and close to that in the other. Her brain must have taken whatever sounds came through and provided a reasonable context for them, though we both know it did not work at all times.

The interesting question of how she could have been functioning was also asked earlier on Monday by the opthalmologist. We knew June had cataracts and that she needed surgery for them, but we didn't realize that she had actually lost about 70% of her vision in one eye and, again, close to that in another. The laser surgeries are planned for the middle of December: one eye one week, and the other one the next. We are glad that we've been able to make and keep these appointments and that the doctors are finding good stuff to do for her. At the same time, nothing goes without at least a little anxiety, so the request for your thoughts and prayers are ongoing.

That will have to be all for the moment. Chances are that, as short as this update is, I probably still managed to forget one or two things I wanted to mention. They'll have to wait for tomorrow or so.

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Tuesday, November 11th 2014

21:17

Peace and the Coming King

  • STATE OF EXISTENCE: somewhat nervous
  • IN THE BACKDROP: NCIS New Orleans

For what it's worth, for those who read my recent FB comment of frustration, I've gone back completely to writing out code on Notepad, and I'm going to try to stay as far away as I can from any wysiwyg programs--at least until I get lazy again.

This week is fairly cluttered for June and me, one of the reasons being doctor’s appointments. Among them is my visit tomorrow to Dr. B, my neurologist, and—as is frequently the case—there’s a bit of anxiety connected to it. I would like to ask for your prayer specifically that I will be able to state clearly (or at least intelligibly) what I am experiencing, and that he would understand and respond patiently. That's not meant to be a reflection on him. He's a really good guy, and I dedicated my Chronicles commentary to him, but I get flustered in communicating with doctors at times. Thanks.

Today (Tuesday) is Veterans Day, a day that is celebrated around here with the rite of the empty mailbox. Around this time it is also frequent practice to have veterans stand up at various public occasions and receive applause. Can we honor veterans in other, perhaps more concrete ways? It’s all very well for us to hang out flags and say “Hurrah for the veterans!” But let me make one quick suggestion, if I may. There are VA Hospital’s in many cities in this country. Many of them are vastly understaffed and can use a lot of volunteer help. I’m going to abstain from any self-serving comments (though I guess I'm implying them), but would like to put forth something for your consideration. If anyone wants to do something for those among our veterans who are really hurting and in need, you might look at exploring the possibility of providing volunteer help at one of those hospitals. Specifically, you could make contact with the chaplain’s office to see if they have anything that you could do. Please note that I’m saying you could, not that you should, but it may be a far more useful way of saying “thank you” than mere gestures. Of course, it will work better if a group gets involved in such a ministry, but (in my experience) there is lots of room for individuals as well.

Wouldn’t it be nice if there were no need for a Veterans’ Day because there weren’t any wars? The Bible promises that there will be peace on earth, and that, perhaps paradoxically, it will be brought about by an extremely powerful and totally autocratic government, namely by God himself. I’m talking about the millennium, when Satan will be bound in chains for 1,000 years, and Christ himself will rule the earth for 1000 years, prior to the final conflict, the last judgment, and the end state of God’s new creation. During the millennium, prophecies such as Isaiah 11:6 will be fulfilled.

As an interlude, if you will permit me, here is an instrumental version of the song, “Peace in the Valley,” written by Thomas A. Dorsey. I put this together a few years ago, and I know I’ve posted it at least once before, but I think it’s appropriate. The lyrics of the last verse (where the harmonica takes the lead) are directly from that passage in Isaiah.

Well, the bear will be gentle, and the wolves will be tame
And the lion shall lay down by the lamb.
And the beasts from the wild shall be led by a little child
And I'll be changed, changed from this creature that I am.

Luke Bible Study

Read the Text!

Bible Reading:
Luke 19:28-40

v. 38 The King who comes in the name of the Lord is the blessed One. Peace in heaven and glory in the highest heaven! (HCSB)

In today’s passage, Jesus very clearly declared that he was the king, the messiah. After all, it was he who sent his disciples into Jerusalem in order to fetch a donkey on which he could ride down into Jerusalem from the Mount of Olives across the Kidron Valley, a path that, not-so-by-the-way, would have led him pretty much straight to the temple. And he told the people who objected to this parade that it was totally necessary. If the people were not allowed to give him acclaim, then the stones would have to take over that role. The recognition of his kingship was essential to his ministry.

Triumphal 
 
Entry

Now, it is also true that Jesus knew that this gesture on his part was not going to lead to the establishment of the messianic kingdom at that time. He was completely aware of the very facts that he himself had predicted, namely, that he would be betrayed, tortured, and killed. He also would have known that he would be resurrected and that he would ascend to heaven. Nonetheless, even though this part of his future was apparent to him, he knew that the people needed to be able to realize that it was their own true king who had been mocked, beaten, and executed. This awareness on the part of the people would come after his death and resurrection.

There is no question, then, that his followers had not yet come to terms with the suffering and atoning aspect of his kingship. Luke tells us in v. 36 that the people were praising God "joyfully with a loud voice for all the miracles they had seen." I imagine that any number of them were hoping for a super-sized miracle once Jesus entered the city. The gospel of John states explicitly that many of the people had come because they were curious to see the person who had raised Lazarus from death. Understanding that fact makes it a little bit easier to see how the crowd — if it was the same people — could turn so quickly from “hosanna!” To “Crucify him!”

The point that I want to make is this: The fact that Jesus had predicted his death and resurrection shows that this entry into Jerusalem, was not a plan gone wrong when he was crucified a week later. Jesus did not expect to take over political power from the Herod clan, the Sadducees, and the Romans and then see his intentions collapse into martyrdom. God did not resort to a secondary contingency plan that utilized Christ’s death as atonement and defeated Satan with a new, and heretofore unplanned, strategy that did not backfire. All of the events — the miracles, his predictions, the demonstration of his kingship, his death on the cross, and his resurrection — were all already included in the reasons for why the Son of God had come to earth.

The triumphal entry was significant, and not an empty celebration that wound up constituting an overture to tragedy. Because Jesus had given so much evidence of his messianic kingship, and, furthermore, that he had done so within the context of demonstrating that he was God incarnate, we know that he went through the events that followed for the sake of reconciling us to God.

1 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Thursday, November 6th 2014

22:56

Day of the Dead

  • STATE OF EXISTENCE: exhausted
  • IN THE BACKDROP: Elementary

Day of the Dead ManilaJoy M., who once upon a time declared herself to be a member of our family—with no objection from us—teaches at an academy in Davao in the Philippines, and in her most recent weekly e-mail she shared some publicly available pictures and information on the observance of the Day of the Dead in that part of the world. Since Filipino culture has been greatly influenced by Mexico, it has also largely taken over the colorful Mexican form of this holiday. Paradoxically, the Day of the Dead only became a nationwide celebration "South of the Border" by political decree during this century. Until then, according to the Wikipedia, it was mostly unknown and unobserved in Northern Mexico.

The entire issue of having one or several days dedicated to the commemoration of the dead presents a cultural enigma. On the one hand, it seems to have been around forever; on the other hand, new versions of it seem to migrate around the globe, supplanting previously established ones.

Day of the Dead ManilaIn the formal calendar of Western Christendom, November 1 has been designated as All Saints Day, which means that special masses are being said for all those who have been beatified (Saints and all of  those who are but one step removed). More specifically that means that they are not in purgatory, but already in heaven. November 2 is reserved for everyone else who died in a state of grace, and special prayers and liturgies are recited on their behalf. A natural aspect of those days has been that people would clean up grave sites as well as to provide candles and flowers, but it has traditionally been relatively low key and definitely church-centered. Nevertheless such acts by the living might just shorten the time that a loved one will have to spend in purgatory.

But, if Jean-Paul Sartre is to be believed—admittedly not an easy supposition—there is a basic human impulse to connect back up with the dead once a year in order to re-immerse oneself in whatever guilt one might feel toward the departed. That’s the notion that’s behind his play, The Flies, according to which once a year all the residents of the town of Argos gather around a cave just outside of town. The priests roll away the big black stone covering the mouth of the cave, and the dead emerge in order to plague the survivors with guilt—real, imagined, and imposed.

Though Sartre is certainly not a great source of information on classical beliefs, let alone their motivations, it seems to me that there have been few advanced cultures, chronologically or geographically, that do not have some special day set aside in order to make sure that the balance between living and dead is maintained properly. The Mexican Day of the Dead and its exported forms in, say, the Philippines or Brazil, have a lot in common with Qing Ming, the Chinese holiday. But we need to distinguish between two aspects of such holidays concerned with the dead, which may or may not be conflated into one festival. Oftentimes, the two categories that I’ll delineate below may be merged on the level of an individual or within a community. However, the two Chinese holidays to which I will refer, will clarify at least in principle what I mean.

Taken in its largest framework, Qing Ming, observed in the spring, is a holiday that celebrates the entire greater family. People will travel to their former homes where relatives are buried. Together the extended family will go out to the graves, clean them up, provide new decorations, set off firecrackers in order to drive off evil spirits, and—very importantly—share a meal with the departed, in which every family member participates. Of course, some of these things are done on a small scale throughout the year, since the dead receive their daily veneration and food offering on the family altar at home, but Qing Ming is a special occasion when the entire family comes out as a unit to pay their respect and supply amenities to those who are no longer with them physically.

Hungry Ghost ShrineIn this context, contemporary English sometimes makes a distinction between “spirit” and “ghost,” and this somewhat arbitrary difference is also maintained in various other languages. We’ll stick with the English. Let us say that a departed soul stands in a reasonably good relationship with the world of the living. He or she receives daily acknowledgement, occasional paper items conveyed to them by burning them, and regular food offerings. The departed is usually referred to as a “spirit,” or its linguistic equivalent. However, spirits who do not get all of the attention to which they are entitled become “ghosts.” In particular, if they have not received their regular feedings, they turn into “hungry ghosts.” Similarly to the dead in Sartre’s play, during Yu Lan Jie, the “Hungy Ghost Festival,” the ghosts emerge and potentially cause problems for people, particularly to those who may have neglected them. Thus, they receive special offering at temporary shrines. People lay out special offerings for them, including food and, once again, burnt paper objects for their subsequent use in the underworld. There are also outdoor stages on which plays are performed for the amusement of the ghosts who will hopefully be in a better mood after they have enjoyed these performances.

Although the Catholic Church encourages prayers to and on behalf of the dead, on the whole it has (at least officially) held the line not to cross over into this mythological level. That is not to say that it was able to banish the belief in vampires in the villages of Romania, for example, but it did, for example, resist the celebration of the Day of the Dead in Northern Mexico until it lost control there. However, where the mythological festivals have become engrained, the Church has made an effort to take a certain amount of ownership so as to re-install a some Christian content into the observances. Alas, syncretism, once established, is very difficult to remove.

Protestants do not officially believe in purgatory, communication with the dead in either direction, or the efficacy of (or, for that matter, the legitimacy of) prayer for the dead. It would seem logical, then, that Protestants have cut all ties with either the liturgical celebrations in their conservative Catholic version or a fortiori any of the stronger feasts of celebration of reunion with the dead. However, it appears that humans quite naturally give in to superstitions and will not easily give up actions done out of anxiety with regard to keeping the dead where they belong. And Protestants are also human, subject to the same temptations and reluctant to eliminate them.

Once a particular ritual has become accepted practice in a community so as to keep the dead from leaving their proper places and roaming around doing harm, are you going to be the one to declare the practice unacceptable and abolish it? What if something evil should follow immediately on the heels of your actions? It takes a strong and determined person to undertake measures that go against the grain of a subconscious fear of the dead as well as the imagined success of maneuvers in defense against them.

In Germany, in the course of the Reformation, a number of principalities abolished All-Saints Day (because German Protestants do not officially venerate saints) and All-Souls Day (because, as mentioned, German Protestants do not subscribe to direct interaction between the living and the dead). I’m specifying Germany here for two reasons: 1) I want to zero in on an area other than England since the Church of England has had a more ambivalent attitude toward the Saints than other regions in Europe, and 2) because of the subsequent event that I’m about to narrate.

Taj MahalIf I may address myself to the married gentlemen reading this, how do you feel about your wife? Only those who might possibly agree with the following description need to answer. You believe that your wife is a veritable angel, a woman of perfect virtue and devotion to God. Only her unblemished soul outshines her external beauty. Indeed, you would conjecture that if anyone breathing on this planet deserves to be called a “saint,” then surely it is she. Sadly, in the case of some couples, she has passed away, and the world is more impoverished by her absence than it will ever know.

If you’re a common, average man, there is not much you can do about maintaining her memory in the future beyond undertaking a few gestures. If you’re Jewish, you an recite the annual Mourner’s Kadish on her Yahrzeit. Perhaps you might inscribe “Racing in Memory of ‘Her Name’” on the side of your sprint car, something I have seen several times, or you might just take out an annual newspaper ad remembering her, but your options are limited. On the other hand, if you happen to be Shah Jahan, the Mughal Emperor of India, you can build the Taj Mahal to honor the memory of your favorite wife and perpetuate her memory centuries later by skilled craftsmen selling stone carved elephants and Taj Mahal snow globes on the premises.

Queen Luise of PrussiaHere’s another possibility for those who wield a certain amount of political power, and it has happened more than once. You are convinced of the genuine saintly qualities of your late wife, but you are not in charge of canonizations. (As King Arthur declared to Lancelot when he conferred knighthood on him in the musical Camelot, “Unfortunately sainthood is not within my power.”) However, there is something else you can do: you can decree that a particular day be set aside annually, on which all the departed (particularly the saintly ones) will be commemorated. And, of course, in your own vicinity, the particular person to whom respect and honor will be paid, will be that irreplaceable wife of yours who was so perfect in her piety.

One instance of establishing such a policy (which, as I said, occurred several times) involved the Prussian King Frederick William III, a Lutheran. He dearly loved his wife Luise, and she was extremely popular with the people. She died in 1810, and the tasks involved in trying to emerge successfully from the earlier defeats by Napoleon kept the king from undertaking any significant internal innovations at first. However, in 1816 he managed to establish the policy that the last Sunday before Advent should be observed as Totensonntag, the Sunday of the Dead. This day would be sufficiently separated from November 1 & 2, not to be confused with the Catholic days, but given over to the memory of Queen Luise, oops, I misspoke, I meant the memory of all the godly deceased. Since Lutheran worship uses a prepared liturgy, it was possible to incorporate some lines of commemoration into the readings for that Sunday.

However, I believe that, on the whole, the king’s intended project did not come to fruition as he had hoped. Totensonntag is observed in Germany to this day. However, it is my perception that the focus of the day was shifted very quickly by the theologians who were in charge of the liturgy to the effect that commemoration of the dead was made to give way in prominence to the hope of the second coming of Jesus Christ and our resurrection in new bodies.

Let me close by quoting the well-known verses on our true future hope, which goes far beyond turning the veneration of death into a party.

1 Corinthians 15:51-55
We will not all fall asleep, but we will all be changed,
in a moment, in the blink of an eye, at the last trumpet.
For the trumpet will sound, and the dead will be raised incorruptible, and we will be changed.
For this corruptible must be clothed with incorruptibility, and this mortal must be clothed with immortality.
When this corruptible is clothed with incorruptibility, and this mortal is clothed with immortality,
then the saying that is written will take place:
Death has been swallowed up in victory.
Death, where is your victory?
Death, where is your sting?

2 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Saturday, November 1st 2014

22:08

ENTRIES ON NUMBERS

  • STATE OF EXISTENCE: okay

Monster EntryThis is just a short message to let everyone know that I have now posted the last four entries on numbers, jointly known as "the monster entry," in correct sequence in a separate location. I need to add navigation and maybe a few more pictures, but you can now read it from the start without scrolling back four days. 

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Friday, October 31st 2014

18:22

The Parable of the 1010 Minas

  • STATE OF EXISTENCE: Okay
  • IN THE BACKDROP: All is quiet on the Trick-or-Treat front.

Hold on! For a much better version of all four parts of this "monster entry," please go to another site where I have collated them and improved on them.

 

Hover your mouse cursor over any number, and its decimal equivalent will pop up. Try it here: 111

It’s Reformation Day, the day on which we remember Martin Luther posting the 10101011111 theses on the door of the castle church in Wittenberg. Here in Hoosierland we celebrate the occasion by having children go from house to house demanding candy from the residents. Actually, lest anyone misunderstand my attempt at being clever, there is no tie-in between the Reformation and Halloween except that it happened to be on this day that Luther made his announcement. It was the day before All-Saints Day, which in English would be called "All-Hallows Eve," and somewhere the idea of ghosts and goblins and trick-or-treating arose, but it had nothing to do with Luther or the Pope. Actually, I don’t think that we’ll have much of a crowd on our front porch today because, as of this moment, it’s cold and rainy outside, and a drastic change in the weather  for the better is not expected for the next few hours.

This is the last part of the Monster Entry, the one in which we go back to Luke. You have probably noticed already that messing around with those number systems has confused my mind more than normally, and I keep accidentally switching between binary, dyadic, and decimal notations. So, please forgive me, and use what you learned in the previous three posts. Keep in mind that there are some overlaps between the systems. For example 1 is 1 in all three systems, 2 is 2 in decimal and dyadic, 3 is 11 in dyadic and binary. If you see a 3 or higher cipher written out, it must be a decimal number (since I’m limiting myself to these three systems). A 2 immediately rules out binary, and a 0 tells us that the number cannot be a dyadic one.

If this is freaking you out, just make use of the hover feature I have installed just for you.

Luke Bible Study Read the Text!

Bible Reading:
Luke 10011:1011-11020

vv. 1011: As they were listening to this, He went on to tell a parable because He was near Jerusalem, and they thought the kingdom of God was going to appear right away.

This parable is clearly very similar to the one recorded in Matthew 11001:1110-11110. Once again, it is true that all things are identical if you ignore their differences, but there are differences, and we should think of them as parables that are alike, but not the same. To be sure, both parables come down to the message that we must be faithful to Christ while we wait for his return, but the setting in Luke also carries political Jesus reality check.

I must tell you that in this long time of working through Luke, I have been surprised by the number of parables whose fundamental interpretation is already given in the text, either by Jesus in reciting it or by Luke in his introductions. In this case, Luke helps us understand the meaning of the parable by noting that Jesus told it in response to his disciples’ expectation that the time had come for him to set up the kingdom of God. We’ll come back to that point presently.

First, though, we need to recognize the fact that Jesus alluded to some real historical events in the story. This observation does not mean that the entire parable is supposed to be a historical narrative; including some historical allusions does not mean that the parable isn’t still a parable. Nevertheless, the way in which Jesus framed it would have struck a chord of recognition in his audience. When King Herod the Great (the baby killer) died in 12 BC, it had only been a few weeks after he had changed his last will to the effect that he named his son Archelaus as his successor. Archelaus was known as a cruel and harsh man, and the populace was afraid of having him as their king, preferring his younger brother Antipas. Archelaus had to travel to Rome in order to have his kingship confirmed by the emperor; he was followed by Antipas, their half-brother Philip, and other messengers opposing his rule. Nonetheless, the emperor Augustus confirmed Archelaus’ position over Judea, Samaria, and Perea, though he did not permit him to carry the title “king.” Instead, he was only allowed to be called “tetrarch,” which means ruler of a quarter of a kingdom, which put him on a par with Antipas, who governed Galilee, and Philip, who received territory further north. Apparently the title “tetrarch” was appropriate even when the land was divided among 11 rulers rather than 100. When Archelaus returned home,  he vented his anger on those who had opposed him within his allocated land by staging a blood bath.

It is important to realize that the close-out of the parable in v. 11011, “But bring here these enemies of mine, who did not want me to rule over them, and slaughter them in my presence,” should not be attributed to God in some sort of analogical fashion, but that they are something that the evil ruler in the parable says. In Jesus’ parable, the man who returned  had become king, though, as we said, Archelaus did not have that title.

There were diverse opinions among first-century Jews as to the attributes of the coming messiah, and not everyone even expected one. But in general, the anticipations included a political mission for the messiah. He would reestablish the Kingdom of David. Thus, as Jesus was heading up to Jerusalem, accompanied by a large parade of people, many of them thought that they were about to witness how Jesus would expel the Romans and take over as the true king.

The details of the parable are fairly straightforward. Before the would-be king left, he gave each of his servants 1010 minas, a unit of weight and currency (weight of the precious metal), whose actual value changed from time to time. It seems to have hovered around 60 shekels, which does not tell you much unless you know that a shekel weighed 211 grams or a little more. The would-be king expected his servants to use that money wisely on his behalf and hopefully make a profit in the process.

When the ruler returned as king, the first servant announced that he had made another 122 minas, and the ruler gave him authority over 1010 towns as a reward. Clearly the realistic basis of the parable ends here. The second servant earned 21 minas, and the king, displaying a fondness for symmetry, put him in charge of 101 towns. A third servant did nothing with the money entrusted to him. In fact, he made use of the occasion to let the ruler know what a bully he was. This man apparently was not very smart. First of all, he should have tried to put the money to work in some way, even if it was nothing more than to put it into a savings account and accumulate interest. Second, given the fact that the ruler was unjust and violent, it would have been best if he had not thrown this accusation at him. The king consigned him among those people who would be executed.

Jesus spoke this parable in light of the fact that a number of his followers expected him to reestablish the kingdom in just a short while. So, how does the parable respond to those hopes? I see 10 points here.

1. Those who belonged to Jesus should be prepared for a lengthy interval before Jesus would actually return as king. It is simply not true that everyone in the early church was living in the anticipation that Jesus would return in a very short time. He could, but he also might not. Please remember that Jesus spoke these words, but that early Christians recorded them and would have had this message right in front of them.

10. During the time of waiting, we should remain faithful to whatever God has called us to be and do. I need to make something clear here. There is no threat to Christians in this parable. The allegiance of the unfaithful servant was against the king, and a Christian’s allegiance is not against Christ. It may take a while yet, but when Christ returns, our standing in him is going to be an occasion for celebration, thanks to his grace.

 

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Wednesday, October 29th 2014

15:39

Numbers, part 3

  • STATE OF EXISTENCE: pooped

Hold on! For a much better version of all four parts of this "monster entry," please go to another site where I have collated them and improved on them.

 

I'm continuing the monster entry. Please read the preceding two entries before this one, or nothing will make sense. Better yet, please go to the link above. My next step was to be to bring this all together in a meaningful way, and I have done so. Thus, I also removed the index that was situated here Once again, here is the index to connect things somewhat.

IV. Dyadic Numbers. Raymond Smullyan has invented an adaptation of the binary system, which he finds more useful for various mathematical reasons. He calls it dyadic notation. It works very much like the binary system, except that it uses 1s and 2s instead of 0s and 1s. The dyadic system, just like the binary system, can express any positive integer, but it does not allow us to write 0.

Again, we have a series of boxes or placeholders, and again, they represent the powers of 2, but each one contains either the designated multiple of 2 or double that amount. There are no empty boxes.

               

PLACES

27

26

25

24

23

22

21

20

2n or

2 x 2n

128 or 256

64 or 128

32 or 64

16 or 32

8 or 16

4 or 8

2 or 4

1 or 2

POSSIBLE VALUES


So, in the far right position we can have either a 1 (20) or a 2 (2 x 20). Counting upwards, you might be tempted to write a “2” as 10 (which would be correct for binary numbers), but, as we said, just as there is no crying in baseball, there is no 0 among the dyadic numbers. A 2 shows up as a “2” in the rightmost box this time (2 x 20).

Under this system, we need to shift boxes to the left whenever the number would be a 3 or higher. So, when we want to write the decimal 3 in dyadic, we can’t put a 3 into the final position, and we must move forward. The dyadic version of 3 is 11: 1 in the 21 (=2) position, and 1 in the 20 position (=1). 4 is 21+ 2 x 1, and we can write it as 12 (one 2 and two 1s). Here are the first twenty integers in Smullyan dyadic style:

Decimal

Dyadic

 

Decimal

Dyadic

 

Decimal

Dyadic

 

Decimal

Dyadic

1 =

1

 

6 =

22

 

11 =

211

 

16 =

1112

2 =

2

 

7 =

111

 

12 =

212

 

17 =

1121

3 =

11

 

8 =

112

 

13 =

221

 

18 =

1122

4 =

12

 

9 =

121

 

14=

222

 

19 =

1211

5 =

21

 

10 =

122

 

15=

1111

 

20 =

1212

Some of the dyadic numbers are the same as their binary counterparts, but constructing them calls for a very different kind of procedure. In binary code, if you want to express the decimal 16, you can just plunk a 1 into the 16-spot and fill out the rest with 0s. But since the dyadic code does not have 0s, that’s not possible. No location can go entirely unfilled until the number is completed. Again, it must get either one or two instances of 2n, as called for by the spot in question. Dyadic numbers can be read as easily as binary ones, but to construct them properly involves a little bit of trial and error, at least for me.

So, if I want to write out my age (65) in dyadic, I can’t just put a 1 into the place for 64, bring in lots of 0s, and then finish with a 1 at the end. In fact, I won’t even need the slot for 64. For binary numbers it’s usually easiest to start from the left. For dyadic numbers we need to do a little more manipulating to make sure that each place has either a 1 or a 2. There are no empty placeholders, and so we may need to do a little planning ahead. If someone reading this discussion has an idea on how to make this process automatic and mechanical, please share it with the rest of us.  

Since the number 65 is odd, we know that it will need a 1 as the last digit, which stands for 20, which, as we said, equals 1.

32

16

8

4

2

1

?

?

?

?

?

1

 

That leaves 64 units to distribute over the row of boxes that we started with 32 on the left. We can do so by allocating them in this way. As mentioned, I arrived at this number by juggling them, so there is no methodology that I know of to walk us through.

32

16

8

4

2

1

1

1

1

1

2

1

111121

To write out the decimal 65 in dyadic, each slot wound up containing one representative, except for the one designated for 2s, where there are two 2s. You might note that, if we were to read the binary and dyadic numbers as decimals, I would be roughly 900,000 years younger in the dyadic format. But that's nonsense and unhelpful, so it's great fun to indulge in. Nevertheless, we must proceed.

The obvious question comes up: What can you do with this? It seems that there is not a whole lot of practical application for grocery shopping or playing music, though dyadic numbers figure prominently in contemporary presentations of arguments leading up to the Gödel Undecidability Principle. But that's something people talk about a whole lot more than use. However, there is a "mathematical" operation you can do with dyadic numbers, which turns out to be fairly intriguing.

Please, if you're sick to death of this math stuff already, skip this next section and wait for the next entry. I don't intend to punish anyone. Of course, if deep down you feel you need to do penance for something, and you consider reading about math penance, by all means, put on the numerical hairshirt.

I'm continuing to give you some highlights out of Smullyan's book, A Beginner's Guide to Mathematical Logic.

What you can do with dyadic numbers is add them up. -- Well, it's not really addition, except we're just literally putting two dyadic numbers together. Smullyan calls it concatenation; we can stick with the English equivalent, "chaining together." Let us conjoin the dyadic versions of 6 and 7. The symbol Smullyan uses for concatenation is an asterisk: *. So, our problem is 6 * 7 (in dyadic) = ?  The dyadic equivalents are: 6 = 22; 7 = 111. Then

22 * 111 = 22111

That's right, we just pasted the two number together and got what appears to be nonsense.

22111 in decimal translates into two 16s, two 8s, and one each of 4, 2, and 1. Then

32 + 16 + 4 + 2 + 1 = 55

and consequently, in decimals again,

6 * 7 = 55

So, in dyadic chaining, if we call the first number x and the second number y,

x * y = "x glued to y" or x y,

and we still want to know what in the world one could possibly find of interest in this apparently meaningless application of our mental super glue.

Yes, there is something of interest, at least if you're fascinated by the way that numbers behave. It might help to know that Smullyan started out his career as a stage magician before turning to mathematics and Daoist philosophy. (Thanks to nephew Michael for pointing out the latter fact to me.) So, let's try some Smullyan magic. By the way, he cautions us to keep in mind that in this case x y does not stand for x multiplied by y (as in xy); that's why I put a space between the two variables.

We are going to start with a really weird move, namely to count the number of ciphers in the dyadic number represented by y. In our example, the number 7 is translated as 111, giving us 3 ciphers, which we're going to designates as L, the Length of the number. Thus,

L of y = 3

L(y) = 3

Now we use L as an exponent for our steady companion, the number 2, and create 2L. In this example, since L = 3,  2L is 23 or 8.

Then we multiply 23 by x, which was 6. So 8 x 6 = 48.

Does this result do anything for us? Can you see anything in that number 48 that could raise our interest?

Let's go back to that very strange number 55, which was the result of chaining 6 and 7. We can ask ourselves, "Is there any kind of significant relationship between 48 and 55?" Something pops up. "What number do we get if we subtract 48 from 55?" The answer is, of course, 7. Now, do you recall the importance of the number 7 in our example? Of course, you do. It's the number that we called y.

Then we get the following equation:

6 x 23 + 7 = 55

So, the general equation for a result of chaining two dyadic numbers together is:

x multiplied by 2L plus y = x and y chained together, or

x x 2L + y = x y

Do you want to try it out with a different set of numbers? Here we go:

3 * 16 = 3 chained to 16

11* 1112 = 111112

We translate the resulting dyadic number:

Dyadic 111112 = Decimal 32 + 16 + 8 + 4 + 2 + 2 = 64.

This time y is 4 digits in Length, so

L(y) = 4

Again the magical formula:

x x 2L + y = x y

Then, in this case:

3 x 24 + 16 =

3 x 16 + 16 =

48 + 16 =

64.

And, of course, 64 (111112) was our result of chaining 3 (11) and 16 (1112) together. Do you thing this is cool? I do.

Just for fun, try some numbers of your own.

I must admit that I'm a little pooped from writing all of this out without wanting to make a mistake or skip a crucial step, so I'm going to wait until the next entry to get back to Luke and the parable.

Not-so-by-the-way, I recommend Smullyan's book. As I intimated above, for a mathematical genius, such as Smullyan, the concept of a "beginner" is often slightly different than for the rest of us. Then again, Smullyan tells us that understanding it may require multiple readings of various passa

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.

Wednesday, October 29th 2014

12:03

Numbers, part 2

  • STATE OF EXISTENCE: Not a 0

Hold on! For a much better version of all four parts of this "monster entry," please go to another site where I have collated them and improved on them.

 

I need to pick up right where the character limit to a blog entry cut me off last night. If you have not read the previous entry, please do so. This won't make a lick of sense without it.

I was discussing binary numbers in preparation for dyadic numbers. In our decimal system, whenever a number in a certain place adds up to more than 9, we move one spot to the left and put in the appropriate digit there. Thus we write 9 as a single digit, but 15 has two digits, where the digit to the left does not stand for 1s but for 10s. With binary numbers, you shift to the left for every time that a 2 comes up. If a 2 belongs into a position, you mark that next spot with a 1. If there is nothing there, you put in a 0. I showed you in the last entry that my age in binary style is

1000001

Let’s now go in the other direction. Say you have won 37 games of "Words with Friends,"and we want to express that number in binary code. We need to reserve enough places that there is room for a 32 as our largest number. We could put a whole bunch of 0’s to the left, but that’s unnecessary because clearly we don't need a 64 or anything higher.

32

16

8

4

2

1

?

?

?

?

?

?

37 is larger than 32, so we can allocate a 1 in the 32 box, subtract 32 from 37, and have 5 left to allocate.

32

16

8

4

2

1

1

?

?

?

?

?

Then, adding a 16 or an 8 would give us a higher number than 37, so they each get 0’s.

32

16

8

4

2

1

1

0

0

?

?

?

Is there room for a 4? Yes; we can put a 1 into the place for 4’s.

32

16

8

4

2

1

1

0

0

1

?

?

 

We have now created our binary number up to 36 (32 + 4), just 1 short of the goal. If we were to put a 1 into the very next spot to the right, that would mean that we were adding a 2, which would give us 38, again too large. So the location for 2’s gets another 0. Now we are looking at

32

16

8

4

2

1

1

0

0

1

0

?

and clearly the last place gets a 1, representing the value of 1.

32

16

8

4

2

1

1

0

0

1

0

1

Thus we have the full binary notation for the decimal number 37:  100101.

One other example. This is the year AD 2014. To write this number in binary style, we need to draw a few more boxes. 1, 2, 4, 6, 8, 16, 32, 64, 128, 256, 512, and 1024. The next higher multiple of 22048, cannot be of any use to us since it exceeds the decimal number we want to express.

1024

512

256

128

64

32

16

8

4

2

1

?

?

?

?

?

?

?

?

?

?

?

 

We put a 1 into the 1024 place and subtract 1024 from 2014,

1024

512

256

128

64

32

16

8

4

2

1

1

?

?

?

?

?

?

?

?

?

?

which leaves us with 990 to fit in. There is plenty of room for 512, so that box gets a 1 as well,

1024

512

256

128

64

32

16

8

4

2

1

1

1

?

?

?

?

?

?

?

?

?

and we still have 478. We can also place a 1 into the box for 256 and subtract that amount from 478.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

?

?

?

?

?

?

?

?

Then we still have 222 to allocate. 222 can accommodate 128, so let’s put a 1 into that location and subtract it from 222.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

?

?

?

?

?

?

?

The remainder is 94. We can add yet another 1 because clearly 64 contributes to the sum.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

?

?

?

?

?

?

 

94 – 64 = 30. Finally we get to write a 0 because 30 is smaller than 32, and, thus, we cannot include 32.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

0

?

?

?

?

?

But 30 definitely leaves lots of room for 16, so we subtract 16 from 30 and have 14, with the 16 spot having earned its 1.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

0

1

?

?

?

?

 

14 contains 8, leaving 6. 8 gets a 1.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

0

1

1

?

?

?

6 is the sum of 4 and 2, so each of those two places get a 1 because they are represented.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

0

1

1

1

1

?

These figures add up to 2014. Since that's an even number we could have marked the 0 in the last spot right at the outset.

1024

512

256

128

64

32

16

8

4

2

1

1

1

1

1

1

0

1

1

1

1

0

Expressed in binary code, we live in the year

AD 11111011110.

Now, I wouldn't have gone through all of this if I didn't want to take a further step and tell you about what I learned from Smullyan's book about dyadic numbers, but that will have to wait. Then I will also talk about a parable that happens to include some numbers.

0 Responses So Far / Comments and Disagreement are Welcome. / Courtesy is Mandatory.